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Article

ERIK DICK

A flux‐difference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertex‐centred finite volume…

Abstract

A flux‐difference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertex‐centred finite volume method. In first order accurate form, a discrete set of equations is obtained which is both conservative and positive. Due to the positivity, the set of equations can be solved by collective relaxation methods in multigrid form. A full multigrid method based on successive relaxation, full weighting, bilinear interpolation and W‐cycle is used. Second order accuracy is obtained by the Chakravarthy‐Osher flux‐extrapolation technique, using the Roe‐Chakravarthy minmod limiter. In second order form, direct relaxation of the discrete equations is no longer possible due to the loss of positivity. A defect‐correction is used in order to solve the second order system.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 1 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

Slawomir Kubacki, Jacek Rokicki and Erik Dick

Applicability of two k‐ω hybrid RANS/LES and a k‐ω RANS models is studied for simulation of round impinging jets at nozzle‐plate distance H/D=2 with Reynolds number 70000…

Abstract

Purpose

Applicability of two k‐ω hybrid RANS/LES and a k‐ω RANS models is studied for simulation of round impinging jets at nozzle‐plate distance H/D=2 with Reynolds number 70000, H/D=2 with Reynolds number 5000 and H/D=10 with Reynolds number 5000 (D is the nozzle exit diameter). The aim is to verify two concepts of unified hybrid RANS/LES formulations, one of DES (Detached Eddy Simulation) type and one of LNS (Limited Number Scales) type in analysis of impinging jet flow and heat transfer. The grid resolution requirements are also discussed.

Design/methodology/approach

The simulations are performed with two k‐ω based hybrid RANS/LES models of very different nature, one of DES type and one of LNS type, and the RANS k‐ω model. For the lower Reynolds number (5000), also dynamic Smagorinsky LES is done. Both hybrid model formulations converge to the same RANS k‐ω model in the near‐wall region and have the same Smagorinsky limit on fine isotropic grids in the LES mode of the hybrid models.

Findings

With the hybrid RANS/LES models, improved fluid flow and heat transfer results are obtained compared to RANS, in the impact region and in the developing wall‐jet region. For accurate predictions at low nozzle‐plate distance, where the impact region is in the core of the jet, it is necessary to sufficiently resolve the formation and breakup of the near‐wall vortices in the jet impingement region and the developing wall‐jet region, as these determine largely the level of fluctuating velocity and the heat transfer. This requires high grid resolution for high Reynolds number, while the grid resolution requirements stay modest for low Reynolds number.

Originality/value

The paper demonstrates that two formulations of hybrid RANS/LES models of different nature, one of DES type and one of LES type, lead to equivalent results. Consistency has been guaranteed in the sense that the RANS limit of both models is the same and that the LES limit on fine, isotropic, grids is the same. In the intermediate range, however, the repartition into resolved and modelled fluctuations may differ considerably.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

Jan Vierendeels, Bart Merci and Erik Dick

Steady‐state two‐dimensional solutions to the full compressible Navier‐Stokes equations are computed for laminar convective motion of a gas in a square cavity with large…

Abstract

Steady‐state two‐dimensional solutions to the full compressible Navier‐Stokes equations are computed for laminar convective motion of a gas in a square cavity with large horizontal temperature differences. No Boussinesq or low‐Mach number approximations of the Navier‐Stokes equations are used. Results for air are presented. The ideal‐gas law is used and viscosity is given by Sutherland’s law. An accurate low‐Mach number solver is developed. Here an explicit third‐order discretization for the convective part and a line‐implicit central discretization for the acoustic part and for the diffusive part are used. The semi‐implicit line method is formulated in multistage form. Multigrid is used as the acceleration technique. Owing to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. By a combination of the preconditioning technique, the semi‐implicit discretization and the multigrid formulation a convergence behaviour is obtained which is independent of grid size, grid aspect ratio, Mach number and Rayleigh number. Grid converged results are shown for a variety of Rayleigh numbers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 4
Type: Research Article
ISSN: 0961-5539

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Article

Bart Merci and Erik Dick

The influence of computational aspects on simulation results is quantitatively investigated for the specific case of a turbulent piloted jet diffusion flame (Sandia Flame…

Abstract

The influence of computational aspects on simulation results is quantitatively investigated for the specific case of a turbulent piloted jet diffusion flame (Sandia Flame D). It is illustrated that, with a fixed turbulence and chemistry model, the results can heavily depend on the numerical aspects. The influence of inlet boundary conditions has already been discussed in an earlier paper. In this work, attention is focused onto the order of accuracy of the spatial discretization in the numerical scheme and onto the position of the outlet boundary. It is stressed that the purpose is not to judge the quality of the applied models, but to illustrate the possible impact of numerical influence factors. The conclusion is a warning message and a demonstration that all numerical aspects must be completely described when calculation results are presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

Jan Vierendeels, Bart Merci and Erik Dick

In this study, Benchmark solutions are derived for the problem of two‐dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right…

Abstract

In this study, Benchmark solutions are derived for the problem of two‐dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right and insulated on the top and bottom boundaries. The temperature differences between the hot and cold walls are large. Neither Boussinesq nor low‐Mach number approximations of the Navier‐Stokes equations are used. The ideal‐gas law is used and the viscosity is given by Sutherland's law. A constant Prandtl number is assumed. The computational method is completely described by Vierendeels et al. Grid converged results with an accuracy of 4 up to 5 digits are obtained for different Rayleigh numbers and temperature differences.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 8
Type: Research Article
ISSN: 0961-5539

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Article

Bart Merci, Jan Vierendeels, Chris De Langhe and Erik Dick

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The…

Abstract

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended scheme is applied to the steady‐state heat transfer of axisymmetric turbulent jets, impinging onto a flat plate. Firstly, the low‐Reynolds version of the standard k‐ε model is employed. As is well known, the classical k‐ε turbulence model fails to predict the heat transfer of impinging jets adequately. A non‐linear k‐ε model, with improved ε‐equation, yields much better results. The numerical treatment of the higher order terms in this model is described. The effect on the heat transfer predictions of a variable turbulent Prandtl number is shown to be small. It is also verified that the energy equation can be simplified, without affecting the results. Results are presented for the flow field and the local Nusselt number profiles on the plate for impinging jets with different distances between the pipe exit and the flat plate.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

Bart Merci, Erik Dick, Jan Vierendeels and Chris De Langhe

Different methods for the determination of accurate values for the dissipation rate ϵ at the inlet boundary of a computational domain, are studied. With DNS data for a…

Abstract

Different methods for the determination of accurate values for the dissipation rate ϵ at the inlet boundary of a computational domain, are studied. With DNS data for a fully developed channel flow and pipe flow, it is shown that the method suggested by Rhee and Sung (2000), in which the kϵ turbulence model is used to compute both k and ϵ from a given velocity profile, is not reliable and can result in very poor results. The method is found to be extremely sensitive to the details of the imposed velocity profile. An alternative procedure is proposed, in which only the ϵ transport equation is employed, with given profiles for the mean velocity and the turbulence kinetic energy. This way, accurate and reliable profiles are obtained for ϵ. Another procedure, based on the turbulent mixing length, was suggested by Jones (1994). The problem. The problem is then shifted towards the determination of the mixing length at the inlet boundary of the computational domain. An expression for this mixing length is proposed in this paper, based on the mentioned DNS data. Finally, the method proposed by Rodi and Scheuerer (1985) is included for comparison reasons. The different procedures are first validated on the fully developed channel and pipe flow. Next, the turbulent flow over a backward‐facing step is considered. Finally, the influence of the inlet boundary condition for ϵ is illustrated in the application of a turbulent piloted jet diffusion flame.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

Krista Nerinckx, Jan Vierendeels and Erik Dick

To present conversion of the advection upwind splitting method (AUSM+) from the conventional density‐based and coupled formulation to the pressure‐based and segregated formulation.

Abstract

Purpose

To present conversion of the advection upwind splitting method (AUSM+) from the conventional density‐based and coupled formulation to the pressure‐based and segregated formulation.

Design/methodology/approach

The spatial discretization is done by a finite volume method. A collocated grid cell‐center formulation is used. The pressure‐correction procedure is set up in the usual way for a compressible flow problem. The conventional Rhie‐Chow interpolation methodology for the determination of the transporting velocity, and the conventional central interpolation for the pressure at the control volume faces, are replaced by AUSM+ definitions.

Findings

The AUSM+ flux definitions are spontaneously well suited for use in a collocated pressure‐correction formulation. The formulation does not require extensions to these flux definitions. As a consequence, the results of a density‐based fully coupled method, are identical to the results of a pressure‐based segregated formulation. The advantage of the pressure‐correction method with respect to the density‐based method, is the higher efficiency for low Mach number applications. The advantage of the AUSM+ flux definition for the transporting velocity with respect to the conventional Rhie‐Chow interpolation, is the improved accuracy in high Mach number flows. As a consequence, the combination of AUSM+ with a pressure‐correction method leads to an algorithm with improved performance for flows at all Mach numbers.

Originality/value

A new methodology, with obvious advantages, is composed by the combination of ingredients from an existing spatial discretization method (AUSM+) and an existing time stepping method (pressure‐correction).

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 16 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

S. Kubacki and E. Dick

This paper aims to provide improvements to the newest version of the k‐ ω turbulence model of Wilcox for convective heat transfer prediction in turbulent axisymmetric jets…

Abstract

Purpose

This paper aims to provide improvements to the newest version of the k‐ ω turbulence model of Wilcox for convective heat transfer prediction in turbulent axisymmetric jets impinging onto a flat plate.

Design/methodology/approach

Improvements to the heat transfer prediction in the impingement zone are obtained using the stagnation flow parameter of Goldberg and the vortex stretching parameter of Wilcox. The third invariant of the strain rate tensor in the form of Shih et al. and the blending function of Menter are applied in order make negligible the influence of the impingement modifications in the benchmark flows for turbulence models. Further, it is demonstrated that for two‐dimensional jets impinging onto a flat plate the stagnation region Nusselt number predicted by the original k‐ ω model is in good agreement with direct numerical simulation (DNS) and experimental data. Also for two‐dimensional jets, the proposed modification is deactivated.

Findings

The proposed modification has been applied to improve the convective heat transfer predictions in the stagnation flow regions of axisymmetric jets impinging onto a flat plate with nozzle‐plate distances H/D = 2, 6, 10 and Reynolds numbers Re = 23,000 and 70,000. Comparison of the predicted and experimental mean and fluctuating velocity profiles is performed. The heat transfer rates along a flat plate are compared to experimental data. Significant improvements are obtained with respect to the original k‐ ω model.

Originality/value

The proposed modification is simple and can be added to the k‐ ω model without causing stability problems in the computations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 8
Type: Research Article
ISSN: 0961-5539

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Book part

Erik Cohen

Three myths of life on other celestial bodies are examined as potential motivators for space tourism. The historical myth of extraterrestrial planetary life was debunked…

Abstract

Three myths of life on other celestial bodies are examined as potential motivators for space tourism. The historical myth of extraterrestrial planetary life was debunked by modern astronomy. The twentieth-century myth-like belief in the existence of stellar civilizations or extraterrestrial intelligence has engendered an extensive search for transmitted signals from such civilizations, but none have yet been detected. The post-modern myth of aliens visiting the Earth by unidentified flying objects, engendered new religious movements; however, it is silent about the aliens’ stellar origins, while the new religions do not encourage adherents to visit the aliens’ abodes. In the final analysis, none of the three myths offers an incentive for space travel and tourism.

Details

Space Tourism
Type: Book
ISBN: 978-1-78973-495-9

Keywords

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